Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
222 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 136 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #10598537 | C2 | direct (N × H) |
| 7. #64877 | C4 | semidirect |
| 9. C2×#3928 | C4 | semidirect |
| 25. #3928 | C2×C4 | semidirect |
| 107. C2×C5 | #1398 | semidirect |
| 123. C5 | C2×#1398 | semidirect |
| 135. C2 | #10598537 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64877 | 2 |
| C2×#64681 | 2 |
| #10598537 | 2 |
| C2×#1398 | 5 |